Critical conditions of saddle-node bifurcations in switching DC–DC converters

Abstract

Although existence of multiple periodic orbits in some DC–DC converters have been known for decades, linking the multiple periodic orbits with the saddle-node bifurcation (SNB) is rarely reported. The SNB occurs in popular DC–DC converters, but it is generally reported as a strange instability. Recently, design-oriented instability critical conditions are of great interest. In this article, average, sampled-data and harmonic balance analyses are applied and they lead to equivalent results. Many new critical conditions are derived. They facilitate future research on the instability associated with multiple periodic orbits, sudden voltage jumps or disappearances of periodic orbits observed in DC–DC converters. The effects of various converter parameters on the instability can be readily seen from the derived critical conditions. New Nyquist-like plots are also proposed to predict or prevent the occurrence of the instability.